I did some FamilySearch, well, searching, and came across an Elizabeth SMITH who seems to fit your description; and I actually think that SMITH is the correct surname. She was born 23 April 1756 in Virginia and died 23 July 1818 (my birthday!) in Ohio. She married her husband, Frederick BONNER (born 4 November 1758 in Dinwiddie; died 23 March 1830 in Ohio, son of Thomas BONNER and Mary HEATH) on 28 September 1779 in Dinwiddie County, Virginia.
Their children included David Smith BONNER (1780-1863) [married to Elizabeth REYNOLDS], Nancy BONNER (1782-1868) [married to Rev. John SALE], Elizabeth BONNER (1783-1873) [married to Dr John TAYLOR], Mary BONNER (1784-1804), Polly BONNER (1784-1800), Chappell Heath BONNER (1786-1873) [married to Anne PELHAM], Martha BONNER (1788-1848) [married to Samuel PELHAM], Stith BONNER (1790-1873) [married to Maria MERCER], and Frederick BONNER (1794-1880) [married to Elizabeth MERCER].
The reason I believe that Elizabeth's SMITH surname is correct is because in this family tree, her mother is named as Barbara SMITH and her siblings include Johanna SMITH (1744-1820) [married to Abednego HALE], Anne SMITH (1753-1795) [married to Daniel TRIGG], Elizabeth Bowker SMITH (1752-1815) [married to Stephen SMITH], Sarah SMITH (1757-????), Guy SMITH (1758-1830) [married to Cornelia DEE], Susannah SMITH (1767-1839) [married to John LEFTWICH], and Catherine SMITH (1771-1835) [married to Thomas CRUTCHER]
Not all of this information is verifiable, however, hopefully, this is helpful to you! Here is the link to Elizabeth's FamilySearch profile: https://www.familysearch.org/tree/person/LZ4L-T8G
As I said, not all of it is verifiable, however, plenty of the profiles DO have sources so hopefully, those are accurate.